With the aid of (REF ), it can be obtained that the \(Q(t)=Q_z\left(t,\pi /2\right)\)  [1]} and \(Q(t)Q(u)=0.5\big [Q_z\left(u,\arctan (u/t)\right)+Q_z\left(t,\operatorname{arccot}(u/t)\right)\big ]\)  [1]} for \(t\ge 0,u\ge 0\) .
Thus, employing (REF ), (REF ) has been expressed as
\(P_{e|\gamma }(x)&=2p\,Q_z\left(a\sqrt{x},\pi /2\right)+2q\,Q_z\left(b\sqrt{x},\pi /2\right)-2p\,q\,\Big [Q_z\left(b\sqrt{x},\arctan (b/a)\right)\nonumber \\ &+Q_z\left(a\sqrt{x},\operatorname{arccot}(b/a)\right)\Big ].\) 
